Author: Quan Yuan, Geoffrey A. Chua, Xing Liu, Youhua (Frank) Chen

Abstract: We study a minimum total commitment (MTC) contract embedded in a finite-horizon periodic-review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per-unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold-commitment-dependent base-stock policy. We also provide a simpler proof of the optimality of the dual base-stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold-commitment-dependent (s, S) policy. We further propose two heuristic policies, which numer ical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.

Keywords: Gradient estimation; Kernel smoothing; Least squares cross validation

This article appears in Production and Operations Management Vol: 24: 11 Pages: 1750-1767. Production and Operations Management is an A-category journal of our college.

Yuan Quan is the first author of this article.